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Truncated dodecahedron
Geomag doesn't come with decagonal panels, so they must be approximated with pentagonal cupolas. There's a rather surprising choice to be made when building this model: which way do I orientate the cupolas? The way shown in the picture, with the cupola's squares joining is the only real choice, because the triangles are slanted at too tight an angle for regular Geomag bars to be used. TODO: what is the angle? (with derivation). Building Instructions The model is straightforward and can be built naturally, although getting started with the first joint is fiddly. There's no internal support needed, and one of the detail shots shows that the angle between the square faces is right at the geomag limit of around 57 degrees. see: flickr set for detail shots, whilst awaiting Wikia support for flickr. The alternative, triangle-to-triangle orientation is, however, the starting point for a startling decomposition: the Drilled truncated dodecahedron (See Karl's photo set on Flickr until that page is created). Another Model I wanted to make my own model of the Truncated Dodecahedron, because I was going to use this model as the starting point to explore ideas about augmenting it with outer cupolae (see Augmented Truncated Dodecahedron). So I photographed the building process and added them here for extra variety for this entry. I've also added notes from my building process, while I'm here editing anyway. This is the same square-to-square model that Karl describes above, just done in different colors. I retained his fine idea to do the decagons in a separate color to highlight the actual Truncated Dodecahedron. Building Instructions As Karl mentions above, "getting started with the first joint is fiddly". As I was assembling the first three pentagonal cupolae, I did have trouble with the floppiness of the parts. It helped to add as many triangles from the Truncated Dodecahedron as early possible, as this did help the stability quite a bit. For further stability while building, I hit upon adding the extra white bars shown below. This helped to keep the cupolae oriented better w.r.t. each other. I did wonder if these white bars could be kept in the completed model for extra stability, and the answer is no. The final model would require the white bars to be shorter than unit length. But for early extra stability during building the first three cupolae, they were a great asset. I had to remove them when I moved on to adding the fourth cupola. Outside view Inside View (with temporary extra supports) Adding the fourth through sixth cupolae was a lot easier, as they started to stabilize each other. It continued to be important to add the triangles from the Truncated Dodecahedron as early possible. Below is a photo of a halfway completed Truncated Dodecahedron, with six cupolae: Truncated Dodecahedron, halfway completed, showing inside The Truncated Dodecahedron was easy to complete after that, adding the final six pentagonal cupolae. Below is a wall-eyed stereo pair of the final result: Left view Right View Related Links * wikipedia:Truncated dodecahedron * Mathworld * Karl Horton's flickr set Category:Polyhedron Category:Archimedean Solid Category:Premium Category:Stereo View